Spear Operators Between Banach Spaces

This monograph is devoted to the study of spear operators, that is, bounded linear operators G between Banach spaces X and Y satisfying that for every other bounded linear operator T:X   →   Y there exists a modulus-one scalar  ω  such that ǁ G +ω T ǁ = 1 + ǁ T ǁ. This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on L ₁ . The